Gothic fiction is typically characterized by mystery as well as elements of the supernatural, and "The Raven" in many ways contains both.
First, the fact that the poem begins on a "midnight dreary" establishes a very mysterious and bleak mood; it seems from the first line that odd and unaccountable things are going to happen. The speaker is filled with "fantastic terrors," and his heart beats quickly in anxiety and fear. We know that he has recently lost a woman he loved, Lenore, and when he suddenly hears a knock at his door, he opens it to find no one there and believes that it could be the ghost of his "lost Lenore." A phantom "rapping" at the door, a sound or which he cannot account through natural means, is certainly gothic.
Then, he hears a tapping at the window, and opens it, letting in a strange black raven who conducts himself like a lord and speaks the word "'Nevermore.'" Like midnight, ravens are associated with mystery and death, and the raven's strange demeanor is likewise mysterious. Although the speaker tries to convince himself that the raven's master must have taught him this word, he cannot help but feel that the bird's "fiery eyes now burned into [his] bosom's core." Thus, the bird seems to have some supernatural powers (or it is all in the speaker's imagination -- either way, it seems real to him). He begins to think that the bird is a "prophet," sent to tell him that he will never reunite with Lenore even after death. However, the raven just sits and never stirs and only repeats the word "'Nevermore.'"
The appearance of the strange bird that portends death, the bleakness of the one word it utters, and the idea that it might be some otherworldly messenger all seem supernatural, and they are certainly mysterious, helping to qualify this poem as gothic.